netShiny Manual

netShiny Manual

Usage

netShiny(Net.obj = NULL, mapping = NULL, resamples = NULL)

Arguments

Net.obj

A list of (sparse) matrices corresponding to the networks that need to be visualized. Net.obj can also be a list of dataframes with data to be used to reconstruct networks. Or, Net.obj can be a combination of (sparse) matrices and dataframes. If items in list are names, these names will be used, otherwise automatic names will be generated.

mapping

A dataframe containing order for each node. There should be a column with the names of the nodes and a column with the corresponding group that the nodes belong to. The app will automatically choose the column representing the grouping of the nodes by looking at the first two columns, and choosing the column with the less number of factor levels as the columns containing the grouping of the nodes.

resamples

If an user has resampling information corresponding to the networks to be visualized the user can also include this in the function, which will incorporate it into the app.

Details

This function opens the shiny app, netShiny. All of the arguments in netShiny are optional, so netShiny can be called without any arguments. Users are prompted with a series of modal dialogs after running the netShiny function. The first modal dialog gives users the possibility to upload files to the app and show the dataframes that already uploaded in a datatable. Users can choose files which contain information to reconstruct networks from them. The next modal dialog let users reconstruct networks using the dataframes that were uploaded. netShiny uses the functions netphenogeno and selectnet from the package netgwas for graph structure learning from non-Gaussian data. The next modal let users optionally choose a file containing the ordering of the nodes. If a dataframe containing the ordering of the nodes was already passed to mapping argument, this modal will visualize this in a datatable. The last modal let users choose the mode they want the app to run in, GxE (Genetic-by-Environment) or general mode. In GxE mode the language used in netShiny is more Genetic-by-Environment related. Users need to input the number of traits if GxE mode is chosen, and optionally, manually input a grouping for the traits.

ET1_Narrabri_1998_Z21 <- read.csv("ET1_Narrabri_1998_Z21.csv", header = TRUE)
ET1_Narrabri_1998_Z65 <- read.csv("ET1_Narrabri_1998_Z65.csv", header = TRUE)
ET4_Narrabri_2002_Z21 <- read.csv("ET4_Narrabri_2002_Z21.csv", header = TRUE)
ET4_Narrabri_2002_Z65 <- read.csv("ET4_Narrabri_2002_Z65.csv", header = TRUE)

In netShiny, users can either input the adjacency/weighted matrices in netShiny, or pass data that still needs to be estimated. We will start with the first way, which is to pass data that still need to be estimated.

df_list <- list(ET1_Till = ET1_Narrabri_1998_Z21,
                ET1_Flow = ET1_Narrabri_1998_Z65,
                ET4_Till = ET4_Narrabri_2002_Z21,
                ET4_Flow = ET4_Narrabri_2002_Z65)
netShiny(Net.obj = df_list)

1. Estimate graph structure using netShiny.

If users have the data loaded as dataframes in netShiny, users can pass the data by saving all of the dataframes in a list. Then, running the function and pass the list containing the dataframes as the Net.ob argument.

The argument Net.obj can be either a list of dataframes that need to be used for network reconstruction or a list of adjacency matrices. The mapping argument needs to be a dataframe containing a column with the names of the nodes and another column with the grouping that the nodes belong to. The resamples argument should be a list, where each entry of the list is also a list containing resampled adjacency matrices for a network.

None of the arguments are required, or dependent on each other. So, users can access the netShiny app by running the netShiny() function with or without arguments in R. If the function is ran without arguments, users can use the built-in functionality in netShiny to browse for the files they want to use for network reconstruction. Network reconstruction is done using the function netphenogeno() from the netgwas package which can be used for graph structure learning for non-Gaussian data. Then, optimal networks are chosen by using the function selectnet(), also from the netgwas package, which chooses an optimal network using an information criterion.

Case Study: Simulated Australian Wheat

To demonstrate the practicality of netShiny, we conducted a case study where we utilized netShiny to analyze and visualize the simulated Australian wheat phenotyping data using the well-known Agricultural Production Systems sIMulator (APSIM) . The data contain 2 different environment types with contrasting water deficiency, no drought and severe drought starting early during the growing season, at two different time stages, tillering and flowering, totalling four different factor levels. The data consists of 20 traits, and 308 genetic markers. The traits are divided into 12 physiological traits, 4 intermediate traits and 4 harvest traits. A more detailed description of the data can be found in . For this purpose, the no drought environment was called ET_1, and the tillering and flowering stage for this environment were denoted as ET1_Till and ET1_Flow, respectively. The severe drought starting early during the growing season was called ET_4, and the tillering and flowering stage for this environment were denoted as ET4_Till and ET4_Flow, respectively. In the next sections, we will show how we carried out the case study using netShiny.

Data Processing

We start by running netShiny() without any arguments in R and use netShiny built-in functionality to load in files.

netShiny()

After running the function, the app opens and prompts users to upload files for network reconstruction, since no arguments were provided. The figure below shows the prompt when netShiny is run without a value for the argument Net.Obj.

Initial prompt.

Users need can choose from a variety of different file formats; .txt, .csv, .xls, or .xlsx. Users can upload multiple files at the same time. netShiny gives users the option to specify for each file separately whether the file has a header, the separator and quote. Users can also choose to exclude certain columns for each of the uploaded files, by entering the column numbers to be excluded, seperated by space, in the “Columns To Exclude (separate by space)” input. The example below shows the case where 4 .csv files were uploaded, and the first two columns were excluded for one of the files. It is important to note that all of the options, header, seperator, quote, and columns to exclude, when changed, only applies to the file that is currently selected in the dropdown menu.

Data shown for uploaded files.

Next, users need to choose method(s) they want to use for network reconstruction. If users choose multiple methods, netShiny will run each method on all the files. This gives users the possibility to compare different methods against each other on the same file. As we stated, netShiny uses the functions netphenogeno() and selectnet() from the netgwas package for network reconstruction and selection of an optimal network, respectively. The netphenogeno() can reconstruct networks using three different methods: Gibbs sampling, approximation method, and a nonparanormal approach. If needed, users can also specify each argument of the netphenogeno() and selectnet() functions. In the figure below an example of this can been where the Gibbs sampling method is chosen. Important to note again is that when users modify an argument, it only applies to the current file that is chosen in the dropdown menu.

Arguments to modify for network reconstruction

If some of the files do not run successfully, netShiny will give users an error notification pop-up in the bottom-right corner, and show which files did not run properly, as shown in the figure below. Users can go back to upload a different file, choose different options for the file upload, or just continue with the files that have run successfully.

Error notification for unsuccessfull netork reconstruction for certain files.

Next, users can optionally upload a file that contains the ordering of the node. The file should contain a column with the names of the nodes and another column specifying which group the nodes belong to. In this case, there should be a column with the names of the markers and another column specifying in which chromosome a marker lays in. In the figure below a file containing the ordering for the nodes is uploaded. netShiny will only look at the first two columns and ignore the other columns. Here too users can change quote, separator, header, and exclude columns for the uploaded files.

The order of the columns is not important for the file containing the mapping of the nodes, netShiny will automatically detect, using the first two columns, which column contains the nodes, and which one contains the grouping.

Uploaded file containing the mapping of the nodes.

For the last step of processing the data, in the GxE mode, users can specify the grouping of the traits. In the general mode, users can use this same feature to assign groups to nodes. In our case, we have 12 Physiological traits, 4 Intermediate traits, and 4 Harvest traits. In the figure below it shows an example after choosing the group names for the traits.

Specified group names for the traits.

Then, users can click on the node names that belong to the trait groups, as shown in the figure below.

Specified group names for the traits.

The netShiny interface is divided into tabs that users can easily navigate. In the following sections we walk through each one of these tabs and explain what information the tabs are meant to convey, using the data we explained in the previous section.

Networks Tab

• After successfully processing the data, the Networks tab is the first tab that users see. This tab is further divided into two subtabs; networks and matrices, with networks subtab selected initially.

Networks Subtab

Figure 1. The Networks tab, at the networks subtab.

Herein, two network are shown simultaneously, with the common nodes of the two networks in the same relative position. The nodes in the graphs are colored to the group that they belong to. The nodes are interactive, giving users the ability to individually reposition each node to their liking. The edges are colored red if the weight of the edge is negative and blue otherwise. The thickness of the edge depends on the absolute value of the weight of the edge; the bigger the absolute value, the thicker the line. All of the nodes shown are nodes that are non-isolated, which are nodes that have at least one connection. Nodes that are isolated are not shown.

There are a plethora of options on what users can do. First, users can interactively change which networks to show in the right and left panel by using the two drop-down menus denoted “left panel” and “right panel” (1). Users can choose to only highlight nodes that belong to a certain group, by choosing the group from the drop-down menu on each of the panels.

There are two ways to interactively create subnetworks in netShiny: by imposing a threshold on the weights of the edges, or by selecting only certain nodes to create subnetworks from. Users can select a threshold for the edges in networks. In the GxE mode, there are two sliders, one controlling the weights of the between markers and markers only, and one controlling the weights between traits to traits, and traits to markers. In the General mode, there is only one slider controlling all of the weights. Choosing a threshold, removes all of the edges that their absolute value are below the selected threshold. Instead of creating subnetworks based on the weights of the edges, users can also create subnetworks by only selecting a subset of nodes, by clicking on the “subnet” button. This then create a subnetwork based only on the selected nodes. It is good to point out, that this option only show edges that are one away from the selected nodes. For example, yield_H was selected as the sole node to create a subnetwork. yield_H has a connection with biomass_H, and biomass_H has a connection with mk1000 whereas yield_H does not. In the subnetwork, where yield_H is the only node selected, the connection between biomass_H and mk1000 will not be shown since this connection is two away from yield_H.

The print button, basically, takes a screenshot of the two networks exactly how they are being shown. After clicking the button, a dialog will show such that users can choose the destination and file name of the picture.

Figure 1. The options available for the customization of the networks.

There are many options where users can customize the networks to their liking. By clicking on the “customize” button, a pop-up dialog will show, with all the options for users to customize. For the nodes, users can choose from the list which contains all of th available nodes, which nodes they want to customize. In the GxE mode, users can choose to only select all of the traits, or all of the markers. Users can change the color, the size, and the font size of the nodes interactively. Users can also choose to show/hide the isolated nodes. In the GxE mode, users can choose to show/hide the markers or traits nodes, individually. There is also a “Reset to default” option, where the networks will return how it was before the changes were applied to them. Next, users can also choose to curve the edges in the networks, by moving the slider, the higher the value, the more curved the edges will be. Next, users can also change the layout algorithm used for the nodes. All of the layout algorithms used are from the igraph package. The default option is “Automatic”, which uses the “layout_nicely” option from the igraph package. If the “Tree” option is selected, users are prompted to also select the root node(s). Users can choose which nodes to make root by either inputting the node by their names, or by the index number of the nodes in the dataset. If multiple nodes is selected, users need to separate the options by a space.

caption

Lastly, if users double click on one of the nodes, it will redirect users to the Weight Analysis tab, with the double-clicked node selected.

Matrices Subtab

The Networks tab, at the matrices subtab.

In the matrices subtab, plots depicting the adjacency matrices are shown. This way, a pattern of networks can be easily seen. The plots are also colored according to the weights. Users can hover on the plots to get more information, for example, which entry is currently being hovered on, and the value of this pairwise connection. Users can also zoom in on the plots. Lastly, users can interactively choose which networks and how many to show by clicking on the menu and selecting which networks to show.

Summary Statistics Tab

In the Summary Statistics tab, summary information about the networks are given. This tab is further subdivided into two subtabs; Metrics and Weight Distribution/Partial Correlations.

Metrics Subtab

The Summary Statistics tab, at the metrics subtab.

The first subtab is the Metrics subtab. Herein, the default plots that are shown are the number of edges, number of nodes, the average clustering coefficient, and the global clustering coefficient for all the networks. This gives users the ability to easily compare these metrics across all the networks. The number of nodes represent the number of non-isolated nodes. Comparing the number of edges and nodes across networks can give users an indication on the density of the networks. For a node, all the other nodes it has a connection with are called its neighbors . Clustering coefficient measures the tendency for a node’s neighbors to be connected to each other . The clustering coefficient that is visualized in the plot is the global clustering coefficient and the average clustering coefficient, which give an indication on how clustered a network is . For both the global clustering coefficient and average clustering coefficient the weights of the edges are ignored. In this subtab it is also possible for users to interactively set a threshold on the weights of the edges, which will then be reflected in the visualizations of the metrics. Users can also choose to select only a few nodes via the subnetwork option.

By default, we only visualize 4 metrics even though there are many other metrics that can be applied to networks. Instead, netShiny affords users the flexibility to manually add functions that they want to apply to the networks. This way we avoid the problem of visualizing many metrics that may not be important to some users and excluding metrics that may be important to other users. Users can manually add functions in the Add statistic bar. The function needs to be able to be applied to an igraph graph object. Users can include the arguments of the function which they need to separate by commas (,). Adding multiple functions is also possible, users can do this by separating the functions with semicolons (;). An example of theMetrics subtab is shown in Figure \(\ref{fig:metrics}\) where we manually add two extra metrics, edge density and mean distance. A path exists between two nodes if there are a sequence of edges connecting these two nodes. The shortest path between two nodes is the path between these two nodes with the least number of nodes you must go through. Mean distance is the average path length of all the shortest distances in a network, and edge density is the proportion of the number of edges and the possible number of edges in a network.

Weights Distribution/Partial Correlations Subtab

The Summary Statistics tab, at the partial correlations subtab.

In the Weights Distribution/Partial Correlations subtab, the distribution of the weights of the edges are shown. The plot contains a facet showing the distribution of the weights for each condition levels. In the figure above, there are four facets containing a distribution plot, since there are four condition levels. Since the weights in this case are partial correlations, the plots then represent the distribution of the partial correlations. Users can select the number of bins for the distribution plot by first clicking on the gears button labeled as 1. in the figure above, and then selecting the number of bins by the input labeled 2. in the figure above.

Similar to the metrics subtab, users can visualize the distribution of subnetworks. Users can select only a few nodes via the subnetwork option, or interactively set a threshold on the weights of the edges by using the options labeled 3. in the figure above. Then, the plot will interactively update to reflect the distribution of the weights on the subnetworks.

Weights Analysis Tab

The Weights Analysis tab.

In the Weights Analysis tab, a barplot with the connections of a node across all the condition levels is shown. The drop-down menu on the left side contains all of the nodes that have at least one connection. Thus, non-isolated nodes are not available to be selected from the drop-down menu. The connections are represented as a barplot. Each bar in the plot represents a connection that the selected node has, and the height of the bars correspond to the weight of the connections. Each facet of the plot corresponds to one of the condition levels. The x-axis are the nodes that the selected node has at least one connection with across one of the conditions levels. The y-axis is the value of the weights. Since the weights of the connections can be really low, especially in GxE applications, making it sometimes difficult to see if a bar is present or not, there are red dots on each bar which makes the connections clear. The plot itself is also interactive where user can hover on top of the bars and get information about a connection.

An example of the Weights Analysis tab is shown in the figure above where the node yield_H is selected, from the drop-down menu marked as 1.in the figure above, and its connections visualized. Here the height of the bars corresponds to the partial correlations of the connections. The bars in the plot are colored according to the corresponding node’s grouping, the legend of the plot is on the right side of the plot. In this case, the bars are colored according to the grouping of the trait or in which chromosome a marker was in. The connections of yield_H is visualized across the condition levels ET1_Till, ET1_Flow, ET4_Till, and ET4_Flow.

Users can also double-click on a node in the networks subtab, which then automatically redirects user to this tab, with the node that was double-clicked on as the selected node.

Centrality Measures Tab

The Centrality Measures tab.

The Centrality Measures tab contain a plot that shows three centrality measures for all the nodes across the networks; the closeness, betweenness, and degree centrality measures. Each facet of the plot corresponds to one of the three centrality measures.The x-axis is the nodes, and the y -axis is the value of the centrality measures. Note that each facet has its own y-axis. For each value on the x-axis, there is one point for each condition levels. For example, in the figure above there are four condition levels, so for each value on the x-axis there are four points, representing the four condition levels. The points are “jittered”, so it is easier for users to distinguish the points from each other.

By clicking on the gears button, which is labeled as 5. in the figure above, user can access more ways to customize the plots. First, users have the option to color the background of the plots according to which group the nodes belong, by clicking on the switch button labeled as 1. in the figure above (this is the default option). In the figure above an example of this is shown, the legends for the grouping of the colors is labeled as 3. in the figure above. Users can also choose where they want the plot legend to be, by clicking on the drop-down menu labeled as 2. in the figure above.

Similar to the summary statistics tab, users can choose to apply the centrality measures on the subnetworks. Users can select only a few nodes via the subnetwork option, or interactively set a threshold on the weights of the edges by using the options labeled 4. in the figure above. Then, the plot will interactively update to reflect the centrality measures on the subnetworks.

Net Diffs Tab

The Net Diffs tab contains five subtabs that illustrate the difference between the networks through different visualization methods. The five subtabs are: Difference Networks, Difference Table, Network Distances, Venn Diagram, and Nodes Sets.

Difference Networks Subtab

The Net Diffs tab, at the difference networks subtab

In the Difference Network subtab a network depicting the differences in edges between two chosen networks is shown. If there is an edge between the same two nodes in the first chosen network but not the second network, then in the network depicted a red edge would appear between these two nodes, suggesting that an edge was lost in the second network compared to the first network. A green edge will be shown between the same two nodes if there is an edge between the two nodes in the second chosen network but not the first one. If in both the first and second chosen network there is an edge between two nodes, but the weight of the edge was positive in the first network and negative in the second, or vice versa, this edge will be shown in blue.

Difference Table Subtab

The Net Diffs tab, at the difference table subtab.

Network Distances Subtab

The Net Diffs tab, at the network distances subtab.

In the Network Distances subtab, pairwise differences between the adjacency or weighted matrices of the networks are illustrated using the norms Euclidean, Manhattan, or Canberra. As shown in the figure above, this subtab is divided into two sections. The first section of the subtab contains a table showing all the pairwise distances between the networks. For example, in the figure above, the distance labeled 2. in the figure above shows the distance between the networks ET1_Flow and ET4_Till to be 14.56. The title of the section labeled as 1. in the figure above, tells users which type of matrix and which distance norm is currently being applied.

The Net Diffs tab, at the network distances subtab.

Users can choose the norm they want to use and whether to use the adjacency matrix (the 0/1 matrix) or the weighted matrix representation of the networks. To change these, users can click on the gears button labeled 1. in the figure above. and either click on the “Adjacency” or “Weighted” option to change with matrix the distance norm should be applied to the matrices.

The Net Diffs tab, at the network distances subtab. Section Network Distances Table.

In the second section a plot showing the distances between the networks for each network separately, is shown. Users can choose multiple norms at the same time to visualize distances between networks simultaneously. In Figure \(\ref{fig:net_dist}\) the Network Distances subtab for the networks is shown. As shown, the title of the sections illustrates whether the adjacency or weighted matrix representation of the networks are used, and which norms are being used to compare distances. The pop-up shows the changes that users can choose for the plots in the bottom section.

Venn Diagram Subtab

The Net Diffs tab, at the venn diagram subtab. Section Network Distances Plot.

In the Venn Diagram subtab, a Venn diagram between the networks is shown. In the example shown above, all four networks were selected. Users can choose to be shown a venn diagram for the nodes of the selected networks, or for the edges of the selected networks. To switch from Venn diagrams of edges to nodes, users can click on the gears button labeled 1. in the figure above, and then clicked on the switch button labeled 2. to interactively switch between edges or nodes for the Venn diagram. Users can also choose which networks to include in the Venn diagram by selecting the networks in the list labeled 3. in the figure above. Note that a minimum of two networks needs to be selected, and a maximum of 6 networks can be selected at the same time.

The shade of the region in the venn diagram represents the number of nodes (or edges) that those networks have in common, the darker the shade of red, the more nodes/edges in common they have. The absolute number and percentage of the nodes/edges they have in common is also shown. Networks have edges in common if there exist an edge between two nodes in all of the networks. In this case, when we say the networks have nodes in common, we mean that a node is present with at least one connection, in all of the networks representing that region. So, more appropriately, the venn diagram of nodes shows a venn diagram of the non-isolated nodes.

Nodes Sets Subtab

The Net Diffs tab, at the nodes sets subtab.

In the Nodes Sets subtab a set operation on the nodes of two chosen networks is shown in a table. This way users can look up in a table which nodes two networks have in common (intersection), all the nodes that come in one or both networks (union), and which nodes are in a certain network but not in the other (complement). Users can choose to select only a few nodes via the subnetwork option. It is also possible for users to interactively set a threshold on the weights of the edges, which will then be reflected in the table. In Figure \(\ref{fig:nodes_sets}\) an example output from the Nodes Sets subtab is shown for the intersection of nodes between the networks ET1_Till and ET4_Till. The threshold for the slider that controls the connections between both trait to trait and trait to markers is set to 0.06 and for the slider that controls the connections between markers to markers only it is set to 0.07.

Comunity Detection Tab

Next, we have the Community Detection tab. This tab is meant to give users the opportunity to see how different community detection algorithms perform on the networks. This tab is further divided into two subtabs: Communities and Modularity.

Communities Subtab

The Community Detection tab, at the communities subtab.

The Communities subtab clusters the nodes of the network based on a chosen clustering algorithm. Different community detection algorithms that each can return a different grouping of the nodes are implemented. The networks in this tab have the exact same layout as the networks in the networks subtab. Much of the ways that users can control these networks is the same as the networks in the Networks tab. Thus, users can choose to select only a few nodes via the subnetwork option. It is also possible for users to interactively set a threshold on the weights of the edges. Users can also change the curviness of the edges. But, since the coloring of the nodes depends on the community detection algorithms, users cannot customize the nodes. An example of this subtab is given in the figure above where the fast greedy modularity optimization algorithm is used to group the nodes and color the nodes accordingly.

Modularity Subtab

The Community Detection tab, at the modularity subtab.

In the Modularity subtab users can look at a plot containing the modularity measurements for different community detection algorithms. In the figure above, each bar in the plot represents the modularity of one of the networks. By default, plots showing the modularity for the fast greedy modularity optimization algorithm and the modularity for the leading eigenvector method are shown. It is possible for users to manually add more community detection algorithms, using the options labeled (1.) in the figure above, where users can input more functions in the same way that was show in the metrics subtab section. netShiny then automatically gets the modularity for all the networks.

Uncertainty Check Subtab

The Uncertainty Check tab.

In the tab Uncertainty Check, the underlying uncertainty of each connection across the networks can be evaluated. There are two options on how the plots can be displayed. The first option is for the users to provide the bootstrapping data as a list of list, as explained above. If users have provided raw data to be estimated in netShiny, then users can also perform bootstrapping in netShiny. Users can choose the number of samples that need to be perform for the bootstrap procedure, and the arguments for the functions. Since this can take a long time, users can start the procedure and continue using the rest of the app without interruption. When the procedure is done, users will get a notification.

In our case, we already performed a bootstrapping analysis beforehand with the Gibbs sampling method of netphenogeno(). Since we have four different conditions, the list containing the bootstrapping information is a list of length four, with each entry representing bootstrapping information of one of the conditions. Each entry containing the bootstrapping information of a network, is also a list. The length of this list is the number of bootstrap samples. Since we have 200 bootstrap samples, the length of this list is 200, with each entry being an adjacency matrix. An example code to perform this procedure is shown below.

n_boots <- 200
n_conditions <- 4
bootstrap_full <- vector("list", n_conditions)
bootstrap_step <- vector("list", n_boots)

set.seed(123) #for consistent results

for (con in 1:n_conditions) {
  for (boot in 1:n_bootstraps) {
    dat <- df_list[[con]] #Get the dataframe from the list we defined above
    n_row <- nrow(dat)
    row_ind <- sample(1:n_row, n_row, replace = TRUE) #Sample the same amount of row as dataframe, with replacement
    dat_sample <- dat[row_ind, ]
    result <- netgwas::netphenogeno(dat_sample)
    result <- netgwas::selectnet(result)
    bootstrap_step[[boot]] <- result$opt.adj #Get the adjacency matrix from the list of result
  }
  bootstrap_full[[con]] <- bootstrap_step
  bootstrap_step <- vector("list", n_boots)
}

rm(bootstrap_step, result)

In the Figure above, certain bars have a red diamond shape on top. These are connections that were estimated to have a connection in the respective networks. An example of this is shown in the figure above for when the trait yield_H was selected. The x-axis is all of the other traits and markers that yield_H had at least one connection with in any of the bootstraps, in and of the conditions. In ET1_Till, the bar for mk0472 has a red diamond on top, this is because in ET1_Till, there is an edge between yield_H and mk0472. Similarly, in ET1_Till the bar for mk0636 has no red diamond on top, this is because in in ET1_Till there is no edge between yield_H and mk0636.

The y-axis of the plot gives the certainty of the connection of the selected node. When you hover on a bar, the node name and certainty for the corresponding node (with the selected node) is shown. In the figure above, the certainty of yield_H and mk0472 is 49.5, meaning, that in 49.5% of the bootstraps, yield_H had a connection with mk0472.